We describe a coupled cluster framework for coupled systems of electrons and harmonic phonons. Neutral and charged excitations are accessed via the equation-of-motion version of the theory. Benchmarks on the Hubbard-Holstein model allow us to assess the strengths and weaknesses of different coupled cluster approximations, which generally perform well for weak to moderate coupling. Finally, we report progress toward an implementation for ab initio calculations on solids and present some preliminary results on finite-size models of diamond with a linear electron-phonon coupling. We also report the implementation of electron-phonon coupling matrix elements from crystalline Gaussian type orbitals within the PySCF program package.